Refraction at a Spherical Surface The left end of a long glass rod, 6.00 cm in d

Question

Refraction at a Spherical Surface The left end of a long glass rod, 6.00 cm in diameter, has a convex hemispherical surface 3.00 cm n radius. The refractive index of the glass is 1.60. Determine the position of the image of an object placed in air on the axis of the rod infinitely far from the left end of the rod Express your answer in centimeters to three significant figures. Determine the position of the image if an object is placed in air on the axis of the rod 13.0 cm to the left of the end of the rod. Express your answer in centimeters to three significant figures. Determine the position the image if an object is placed in air on the axis of the rod 4.00 cm from the left end of the rod. Express your answer in centimeters to three significant figures.

Explanation / Answer

Formula :-        n2 / v   -   n1 / u   =   (n2   -   n1) / R

   where      n1   =   refractive index of first media (air)   =   1.00

                  n2   =   refractive index of first media (glass)   =   1.60

                  v   =   distance of image from refractive surface    =   sb

                  u   =   distance of image from refractive surface ( - ve if object lies to the left)

                  R   =   radius of curved surface   =   3.00   cm

Part- a.

  given   u   = infinity

      n2 / v   -   n1 / u   =   (n2   -   n1) / R

         =>   1.60 / sb   -   1.00 / infinity =   (1.60   -   1.00) / 3.00

         1.60 / sb   =   0.60 / 3.00

   position of image      sb =   8.00 cm

   i.e. image is formed at 8.00 cm, to the right of curved surface.

Part- b.

  given   u   =   -13.0 cm

         =>   1.60 / sb   -   1.00 / (- 13.0)   =   (1.60   -   1.00) / 3.00

         1.60 / sb   =   0.60 / 3.00   -   1.00 / 13.0

         1.60 / sb   =   0.123

   position of image      sb   =   1.60 / 0.123

                                       =   13 cm

   i.e. image is formed at 13 cm, to the right of curved surface.

Part- c.

   given   u   =   - 4.00

         =>   1.60 / sb   -   1.00 / (- 4.00)   =   (1.60   -   1.00) / 3.00

         1.60 / sb   =   0.60 / 3.00   -   1/4.00

                        =   - 0.05

   position of image      sb   =   1.60 / ( - 0.05)

                                       =   - 32.0   cm

   i.e. image is formed at 32.0 cm, to the left of curved surface, as the sign is - ve.

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